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  • How many 3 - letter words with or without meaning, can be formed out of the letters of the word, 'ALGORITHMS', if repetition of letters is not allowed?

How many 3 - letter words with or without meaning, can be formed out of the letters of the word, 'ALGORITHMS', if repetition of letters is not allowed?

Option: 1

120


Option: 2

360


Option: 3

930

 


Option: 4

720


Answers (1)

The word 'ALGORITHMS'' has 10 different alphabets

Hence, the number of 3-letter words (with or without meaning) formed by using these letters is given by,

\begin{aligned} &{ }^{10} P_3=\frac{10 !}{(10-3) !}\\\\ &{ }^{10} P_3=10 \times 9 \times 8\\\\ &{ }^{10} P_3=720 \end{aligned}

Therefore, the number of ways the letter is formed is 720 ways.

Posted by

Sumit Saini

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